**Parallel &**

Perpendicular Lines

Perpendicular Lines

A

transversal

is a line that intersects two or more coplanar lines at distinct points.

Lines and Angles

What is the measure of each angle?

Justify each answer.

Properties of Parallel Lines

A

flow proof

uses arrows to show the logical connections between the statements. Reasons are written below the statements.

Proving Lines Parallel

Parallel and Perpendicular Lines

The measure of an exterior angle of DEF is 4x. The measure of one of this angle’s remote interior angles is x + 23. The measure of the other remote interior angle is 2x + 12. Find the value of x, the measure of each angle of the triangle, and the measure of the exterior angle.

Parallel Lines and Triangles

Identify all pairs of each type of angle in the diagram below.

1) corresponding angles

2) same-side interior angles

3) alternate interior angles

4) alternate exterior angles

Decide whether the angles are alternate interior angles, same-side interior angles, corresponding angles, or alternate exterior angles.

5) 6)

7) 8)

The map at the below shows the intersection of Maple Street and Oak Street by Main Street. Name the angle pairs represented by the locations listed below.

a. town hall and gas station

b. school and library

c. library and post office

d. school and gas station

Describe the statement as true or false.

If false, explain.

Find the value of x and y.

Then find the measure of each labeled angle.

Find the value of x and y.

Then find the measure of each labeled angle.

Find the value of x and y.

Then find the measure of each labeled angle.

Determine the value of x for which r || s. Then find the measure of each labeled angle.

Determine the value of x for which r || s. Then find the measure of each labeled angle.

Determine the value of x for which r || s. Then find the measure of each labeled angle.

Use the given information to determine which lines, if any, are parallel. Justify each conclusion with a theorem or postulate.

Determine the value of x for which r || s. Then find the measure of each labeled angle.

Complete this paragraph proof of the Perpendicular Transversal Theorem (Theorem 3-9).

A developer is planning a new housing complex. The map of the complex is shown at the right. Assume that all streets lie in a plane.

a) If Washington and Lincoln Streets are to be parallel, what must be true of 1 and 2?

b) Which streets must be parallel if 3 4 Justify your answer.

c) If m 1 = 90 and your answers to parts (a) and (b) are true, to what roads is Eagle Road perpendicular?

Find the value of each variable.